Structural Integrity Invariant Ψ in 12-Dimensional Numerical Systems

This work presents Version 3 of the Structural Integrity Invariant Ψ, extending the framework to a twelve-dimensional (12D) numerical setting. The invariant Ψ is defined as a dimension-independent structural measure that evaluates the internal coherence of numerical systems through scale, distribution, spectral, and geometric components. The formulation remains invariant under dimensional extension, demonstrating that structural integrity is not a byproduct of dimensionality but a fundamental property of numerical organization. The 12D extension serves as a non-physical, apolitical mathematical testbed, illustrating the stability, convergence, and robustness of the invariant under higher-dimensional configurations. No physical assumptions are imposed; the construction is purely mathematical and computational. This version supersedes previous lower-dimensional formulations and establishes a generalized pathway toward arbitrary n-dimensional structural analysis of numerical systems.